Power management in a cellular system

ABSTRACT

A method of controlling the respective transmit powers allocated by a base station of a cellular communications network to each of a plurality of sub-bands is provided. Information from at least one other base station of the network is received, the information comprising information about a sensitivity of a utility function in a cell served by the other base station to changes in powers allocated to respective sub-bands by the base station. A sub-band is identified in which it would be relatively advantageous to increase a transmit power. It is determined whether a factor relating to a happiness of users in the cell exceeds a threshold value. The transmit power in the identified sub-band is increased only if the happiness factor is less than the threshold value.

This invention relates to a cellular telephone network, and inparticular to methods for controlling the power of signals transmittedby base stations within such a network, in order to reduce theinterference effects of such transmissions, while maintaining requiredperformance of the network. The invention also relates to base stationsin such a network.

Fourth generation (4G) cellular systems such as the Long-Term Evolution(LTE) are currently being developed in order to improve both systemperformance and user data rate, compared with third generation systems.Although such systems are designed to improve system performance anduser data rate, strong emphasis is given to enhancing system performancefor users at the cell edge. One of the most effective ways to achievesuch improvements is by power and interference management.

While power and interference management is originally designed toincrease systems and user performance by reducing unnecessaryinterference, it is important to realize that this can be achieved byreducing transmit powers as much as possible while still meeting acertain satisfaction objective. By eliminating unnecessary transmitpower, it is possible to significantly improve the energy efficiency.While the energy efficiency for a single base station may not be aserious matter, it is highly relevant if a large network of basestations is deployed.

In a typical deployment scenario, a cell does not exist alone, whichmeans that each cell is likely to be surrounded by neighbouring cells.Thus, as a mobile user moves away from the serving base station towardsa neighbouring cell, the call quality degrades, not only due to theweakening of the serving base station signal, but also the increase ofthe interference coming from the dominant neighbouring cell(s). Suchinterference is often known as inter-cell interference, and themitigation of such interference has been considered, in order to boostthe experience of the cell-edge users. Interference management for LTEis more complicated than in the legacy 3G systems such as the WidebandCode Division Multiple Access (WCDMA) systems, as LTE systems involvethe allocation of power in both time and frequency domains, while WCDMAsystems involve only the time-domain allocation.

One well-known method to mitigate inter-cell interference is via the useof what is known as fractional frequency reuse (FFR), in which mobileusers in the centre of every cell are allocated the same frequency,whereas users at the cell edges are allocated a subset of frequenciesthat are different from those at the edges of the immediate neighbourcell. As a result, the inter-cell interference at the cell edges can besignificantly reduced (R. Kwan, C. Leung, “A Survey of Scheduling andInterference Mitigation in LTE”, Volume 2010, Article ID 273486).

While FFR and its variants are well-known techniques for interferencemitigation, they suffer from the drawback that the subsets offrequencies used for the cell-edge mobile users need to be carefullyplanned, and this planning is typically done statically during thenetwork planning stage. As a result, such methods are not suitable forfemtocells, in which base stations are deployed in an ad hoc manner.Also, these methods do not take into account the dynamic user trafficdistributions, and thereby reduce the efficiency of the spectrumutilization.

On the other hand, it is possible to make the allocation of power andfrequency resources vary dynamically by allocating frequency, power,modulation and coding schemes (MCS) jointly for each user in a cell in acentralized fashion (D. López-Pérez, G. de la Roche, A. Valcarce, A.Jüttner, J. Zhang, “Interference Avoidance and Dynamic FrequencyPlanning for WiMAX Femtocells Networks”, Proc. of ICCS, 2008). However,such an approach requires a centralized entity, and the computationcomplexity is impractically high.

In A. L. Stolyar, H. Viswanathan, “Self-organizing Dynamic FractionalFrequency Reuse for Best-Effort Traffic Through Distributed Inter-cellCoordination”, proc. of IEEE Infocomm, April 2009, a gradient-basedalgorithm is presented, in which the frequency reuse patterns aredynamically adapted to the traffic distribution. As this approach isself-organizing among cells in a distributive fashion, frequencyplanning is not required. Also, this method not only provides a way toassign frequency in a distributive manner, it also allows the power tobe adjusted dynamically in frequency, and thereby provides an extradegree of flexibility. While this approach is useful, the document doesnot provide details regarding how Quality of Service (QoS) can be takeninto account in the formulation. As a result, the power allocation maynot necessarily be appropriate to what the services actually require,thereby reducing the power efficiency. Also, while the document providesa useful framework in dynamic interference mitigation, issues regardingimplementation aspects remain open. For example, the formulation assumesan exact knowledge of the analytical relationship between the spectralefficiency and the signal-to-interference and noise ratio (SINR). Inpractice, there is no such fixed relationship, due to the fact thatdifferent vendors may have their own receiver implementation, and,therefore, different performance.

According to an aspect of the present invention, there is provided amethod of controlling the respective transmit powers allocated by a basestation of a cellular communications network to each of a plurality ofsub-bands, the method comprising:

-   -   receiving information from at least one other base station of        said network, said information comprising information about a        sensitivity of a utility function in a cell served by said other        base station to changes in powers allocated to respective        sub-bands by said base station,    -   identifying a sub-band in which it would be relatively        advantageous to increase a transmit power;    -   determining whether a factor relating to a happiness of users in        the cell exceeds a threshold value; and    -   increasing the transmit power in the identified sub-band only if        the happiness factor is less than the threshold value.

According to an aspect of the present invention, there is provided amethod of controlling the respective transmit powers allocated by basestations of a cellular communications network to each of a plurality ofsub-bands, the method comprising:

-   -   transmitting information from a first base station to at least        one other base station of said network, said information        comprising information about a sensitivity of a utility function        in a cell served by said first base station to changes in powers        allocated to respective sub-bands by said other base station,    -   wherein said step of transmitting information comprises        transmitting information to the at least one other base station        over an X2-interface.

A method of controlling the respective transmit powers allocated by basestations of a cellular communications network to each of a plurality ofsub-bands, the method comprising:

-   -   transmitting information from a first base station to at least        one other base station of said network, said information        comprising information about a sensitivity of a utility function        in a cell served by said first base station to changes in powers        allocated to respective sub-bands by said other base station,    -   wherein said step of transmitting information comprises        transmitting information relating to the Relative Narrowband        Transmit Power of said cell in each of said sub-bands.

According to an aspect of the present invention, there is provided amethod of determining an effect of interference in a cell served by abase station of a cellular communications network, said interferencebeing caused by transmissions from a base station in at least oneneighbouring cell of said network, the method comprising:

-   -   obtaining measurements from mobile devices connected to the base        station; and    -   using the measurements to derive a measure of the sensitivity of        a utility function in said cell served by said base station to        changes in powers allocated to respective sub-bands by said        other base station.

According to an aspect of the present invention, there is provided amethod of estimating a spectral efficiency of a sub-band in a basestation on a cellular communications network, the method comprising:

-   -   approximating the spectral efficiency by a power function of a        Channel Quality Indicator reported by a mobile device making        measurements on that sub-band;    -   approximating the Channel Quality Indicator by a linear function        of a Signal to Interference and Noise Ratio measured by the        mobile device, wherein the Signal to Interference and Noise        Ratio is measured in decibels.

According to an aspect of the present invention, there is provided amethod of controlling a base station in a cellular communicationsnetwork, the method comprising:

-   -   for each of a plurality of users, receiving a value representing        an initial bit rate requirement for said user;    -   determining a respective downlink power required to be allocated        to said users to achieve said respective bit rate requirements;    -   determining a total downlink power requirement as a sum of said        respective downlink powers required; and    -   when a total downlink power of the base station exceeds a        threshold value, reducing a bit rate requirement for at least        one of said users to a value below the respective initial bit        rate requirement.

According to an aspect of the present invention, there is provided amethod of calculating a value for a load on a base station of a cellularcommunications network, wherein the base station can use a plurality ofsub-bands and can use frequency-selective power control, the methodcomprising:

-   -   calculating a value for the load, based on the average power and        the average bit rate for each user.

According to an aspect of the present invention, there is provided amethod of controlling the respective transmit powers allocated by a basestation of a cellular communications network to each of a plurality ofsub-bands, the method comprising:

-   -   in the base station, obtaining channel quality information from        mobile devices connected to the base station;    -   for each sub-band, forming an average channel quality measure        using channel quality information from said mobile devices; and    -   from said average channel quality measures, estimating        information about a sensitivity of a utility function in a cell        served by said base station to changes in powers allocated to        respective sub-bands by other base stations.

According to an aspect of the present invention, there is provided abasestation adapted to perform the method of any other aspect.

For a better understanding of the present invention, and to show how itmay be put into effect, reference will now be made, by way of example,to the accompanying drawings, in which:—

FIG. 1 shows a part of a cellular communication network, operating inaccordance with fourth generation (4G) cellular standards such as theLong-Term Evolution (LTE).

FIG. 2 shows a base station in the network of FIG. 1.

FIG. 3 is a diagram illustrating the effect of considering a happinessfactor.

FIG. 4 is a diagram illustrating the effect of considering a modifiedhappiness factor.

FIG. 5 is a flow chart, illustrating a first method in accordance withthe invention.

FIG. 6 illustrates a change in utility over time, for various values ofa scaling factor.

FIG. 7 illustrates a change in power over time, for various values ofthe scaling factor.

FIG. 8 is a flow chart, illustrating a second method in accordance withthe invention.

FIG. 9 illustrates a change in utility over time, for various values ofa scaling factor.

FIG. 10 illustrates a change in power over time, for various values ofthe scaling factor.

FIG. 11 illustrates a relationship between Signal to Interference andNoise Ratio, a Channel Quality Indicator, and spectral efficiency.

FIG. 12 further illustrates a relationship between Signal toInterference and Noise Ratio, a Channel Quality Indicator, and spectralefficiency.

FIG. 13 illustrates the available connections between base stations in apossible deployment of femtocell and macrocell base stations.

FIG. 14 illustrates frequency allocations in possible deployments offemtocell and macrocell base stations.

FIG. 15 illustrates relationships between utility, power and requiredbit rate.

FIG. 16 is a second illustration of the relationships between utility,power and required bit rate.

FIG. 1 shows a part of a cellular communication network 10, operating inaccordance with fourth generation (4G) cellular standards such as theLong-Term Evolution (LTE). The network 10 includes macrolayer basestations, or enhanced Node B's (eNBs), 12, 14, serving respective cells16, 18, it being appreciated that there is a region of overlap betweenthe two cells 16, 18, in which a user equipment device would be able toestablish a connection with either of the base stations 12, 14.

Located within the cells 16, 18 are a number of femtocell base stations,or Home enhanced Node B's (HeNBs), 20, 22, 24, 26, 28, 30, 32, 34, eachserving a respective cell in its immediate vicinity. As is well known,there may be tens, hundreds, or even thousands of femtocells within onemacrocell. FIG. 1 shows only a small number of such femtocells for thepurposes of clarity. For example, the femtocells might be individuallyowned by customers of the cellular network, or they might be under thecommon management of the premises in which they are located, such as ashopping mall, university campus, office park or large office building.

FIG. 2 shows in more detail the form of one of the base stations in thenetwork. The base station 40 shown in FIG. 1 might be a macrolayer basestation or a femtocell base station.

The base station 40 has transceiver circuitry 42, for converting signalsto and from the formats required for transmission over the airinterface. As mentioned above, in this illustrative example, the basestation is intended to form part of an LTE network, and the transceivercircuitry therefore converts the signals to and from the formatsrequired for this. An antenna 44 is connected to the transceivercircuitry 42.

The base station also has interface circuitry 46, for connection to therest of the network. Where the base station 40 is a femtocell basestation, the interface circuitry 46 might for example be suitable forconverting signals to and from the formats required for transmissionover a broadband internet connection. Where the base station 40 is amacrolayer base station, the interface circuitry 46 might for example besuitable for converting signals to and from the formats required fortransmission over a dedicated link to the core network of the cellularcommunications network.

A modem 48 is connected between the transceiver circuitry 42 and theinterface circuitry 46, for processing the signals and extractingrelevant data therefrom. The modem 48, the transceiver circuitry 42 andthe interface circuitry 46 operate under the control of a processor 50,as described in more detail below.

One of the aspects of the operation of the base station 40 that iscontrolled by the processor 50 is the allocation of users to particularfrequency channels, and the allocation of particular power levels to theavailable channels. Increasing the power of signals to one particularuser will typically improve the service that can be provided to thatuser, for example by increasing the available data rate, but it mightworsen the service that can be provided to other users, for example byincreasing the level of interference that they will detect.

We assume here that we have K cells, with kε{tilde over (K)}={1, 2, . .. , K} and J sub-bands jε{tilde over (J)}={1, 2, . . . {tilde over (J)}}in the system. Furthermore, we assume that each sub-band consists of afixed number of sub-carriers. Also, it is assumed that time is slotted,and that transmissions within each cell are synchronized, so thatintra-cell interference is not present. Two generic quantities areparticularly relevant to an inter-cell interference coordination schemefor LTE-based systems.

The first one is the concept of utility, which generally quantifies thelevel of satisfaction of the entity involved. Let U be a global utilityfunction of the system, which is given by

U=Σ _(k) U _(k).  (1)

It represents the sum of all utility functions among all cells, whereU_(k) is the utility function of cell k, which is given by the sum ofthe utility U_(k,i) among all users for cell k, i.e. U_(k)=Σ_(i)U_(k,i).The idea is to find a way (or ways) to improve, or preferably maximize,the global utility function U.

The second quantity is the transmit power. Here, in the context ofOrthogonal Frequency Division Multiple Access (OFDMA) systems such asLTE, the transmit power is expected to be frequency dependent. LetP_(k,j) be the power allocated in sub-band j of cell k, and the maximumpower cell k can have is P_(k), i.e. Σ_(j)P_(k,j)≦P_(k). The wholeproblem of inter-cell interference coordination reduces to how P_(k,j),∀j is allocated for each k in order to improve or maximize U.

In A. L. Stolyar, H. Viswanathan, “Self-organizing Dynamic FractionalFrequency Reuse for Best-Effort Traffic Through Distributed Inter-cellCoordination”, proc. of IEEE Infocomm, April 2009, a gradient-basedmethod is proposed, in which the global utility is improvedsub-optimally in a distributive fashion. The main idea of the proposedmethod is as follows:

Let D_(j)(m,k)=∂U_(k)/∂P_(m,j) i.e. the rate of change of the utilityfunction U_(k) for cell k, with respect to the transmit power cell m hasallocated for sub-band j. The quantity corresponds to the change of thelevel of satisfaction that a cell m would incur at sub-band j of cell k.For the purpose of discussion, this quantity will also be called the Dvalue for simplicity. Obviously, an increase in P_(m,j) may potentiallyhave negative impact on U_(k) when k≠m (i.e. cell m is a neighbourcell), as such an increase would give rise to additional interference atsub-band j coming from cell m, and vice versa. On the other hand, whenk=m, an increase of power at sub-band j would enhance the signal qualityat this particular sub-band, and would have a positive impact on its ownutility.

It can be noted that D_(j)(m,k) is not very useful if it is consideredin only one cell at a time. However, when it is exchanged amongneighbour cells, it allows the neighbour cells to know the level ofimpact caused in the other cells when a certain power level is allocatedat each sub-band. By receiving D_(j)(m,k) from the neighbour cells, cellk would then aggregate them for each sub-band j, i.e.

D _(j)(k)=Σ_(m) D _(j)(k,m),  (2)

(where the switch of the indices m and k represents the fact that cell kis now the neighbour cell of each of the neighbour cells m), includingthe case of k=m.

In other words, D_(j)(k) corresponds to the aggregate sensitivity of theutility function to all cells due to the perturbation of its owntransmit power at sub-band j.

When D_(j)(k)<0, a positive power increment would incur a negativeimpact on the aggregate satisfaction among all cells, and vice versa.The general idea proposed in the prior art document discussed above isfor cell k to increase the power by selecting a sub-band associated withthe largest positive value of D_(j)(k), and vice versa.

Let δP>0 be a fixed parameter, let P_(k)=Σ_(j)P_(k,j) be the total powercurrently used, and let {tilde over (P)}_(k) be the power limit. In eachof n_(p) time slots, cell k updates the power sequentially as follows:

-   -   1. Set P_(k,j) _(*) =max (P_(k,j) _(*) −δP, 0), where j_(*) is        the sub-band index, such that D_(j) _(*) (k) is the smallest        among all j's, given that D_(j)(k)<0 and P_(k,j)>0.    -   2. If P_(k)<{tilde over (P)}_(k), set        P_(k,j*)=P_(k,j*)+min({tilde over (P)}_(k)−P_(k), δP), where j*        is the sub-band index, such that D_(j*)(k) is the largest among        all j's, where D_(j)(k)>0.    -   3. If P_(k)={tilde over (P)}_(k), and max_(j) D_(j)(k)>0, set        P_(k,j) _(*) =max (P_(k,j) _(*) −δP, 0), and        P_(k,j*)=P_(k,j*)+min(P_(k,j) _(*) ,δP), where D_(j) _(*) (k)        and D_(j) _(*) (k) are the largest and smallest among those j's        which are P_(k,j)>0 and D_(j) _(*) (k)<D_(j) _(*) (k).

In this illustrated embodiment, the downlink power adjustment algorithmtakes account of the quality of service (QoS) experienced by the users.

A common utility function for cell k is typically defined as the sum ofthe logarithms of the average bit rates over all users within the cellk. This utility function is rooted in economics, and is motivated by thefact that a fixed increase in bit rate is more important for low bitrate than for users who are already enjoying a high bit rate. Anotheradvantage of such a function is that it is smooth and continuouslydifferentiable, thereby simplifying the complexity in computing theutility sensitivity. Despite the above advantages, such a utilityfunction does not readily provide a means to incorporate QoS into thepower adjustment mechanism. For example, consider three users served bya base station, having bit rates of 1 Mbps, 2 Mbps, and 3 Mbpsrespectively. If all three users only require a bit rate of 500 kbps, itmay not be efficient to provide more than necessary from the point ofview of resource utilization. An unnecessarily high power generates anunnecessary level of interference, which would then have a knock-oneffect on the neighbouring cells. In order to maintain a good level ofsatisfaction, the neighbours would require a higher power, therebyboosting the overall background interference. The reverse is also true:if a base station reduces its power to a level which just meets the userbit rate requirements, the level of interference to its neighbours wouldreduce. The neighbours, in turn, would require less power to maintainthe call quality, thereby emitting lower interference to the originalbase station. As a result, the original base station, in turn, wouldthen need less power to maintain the call quality. This processcontinues until the background interference, and, therefore, thetransmit powers of all base stations, eventually settles to a lowerlevel.

The implication of the above process is important, as the idea ofremoving unnecessary power provides a “feedback” mechanism whicheventually helps to further reduce the power requirement for a fixed QoSdue to the lowering of the overall interference. This lowering of thepower requirement translates to an energy saving for the network.

One way to take the QoS into account is to modify the utility function.However, such an approach potentially makes the utility function morecomplex, and thereby complicates the sensitivity calculation. In thisembodiment, we quantify whether a user's expectation is met by aquantity known as the “Happiness Factor”, H_(k,i), which is given by:

$\begin{matrix}{H_{k,i} = \frac{{\overset{\_}{R}}_{k,i}}{{\overset{\sim}{R}}_{k,i}}} & (3)\end{matrix}$

where:R _(k,i) is the averaged bit rate achieved by user i in cell k, and{tilde over (R)}_(k,i) is the corresponding bit rate requirement, whichcan be directly proportional to the guaranteed bit rate (GBR) (forexample as discussed in 3GPP TS 36.413, S1 Application Protocol (S1AP),Release 9, v9.5.1) or can be some function of the GBR.

When H_(k,i)>1, the user is experiencing a bit rate that exceedsexpectation. The opposite is true when H_(k,i)<1. Let H_(k) ^((n)) bethe weighted n-th moment of happiness of cell k, i.e.

$\begin{matrix}{{H_{k}^{(n)} = {\frac{1}{N_{k}}{\sum\limits_{i = 1}^{N_{k}}\; {w_{k,i}H_{k,i}^{n}}}}},} & (4)\end{matrix}$

whereN_(k) is the number of users in cell k, andw_(k,i) is a cell-specific weight for user i in cell k.

This weight can be used to bias the emphasis among users within thecell, and follows the constraint

${\sum\limits_{i = 1}^{N_{k}}\; w_{k,i}} = {N_{k}.}$

As a special case, when w_(k,1)=w_(k,2)= . . . =w_(k,N) _(k) =1, H_(k)=H_(k) ⁽¹⁾ reduces to a simple arithmetic mean.

Note that H _(k)=1 implies that the average happiness for cell k meetsthe expectation. However, it also implies that some users are belowexpectation, while some are above expectation. While the average isuseful to quantify performance in general, a more refined approach is toprovide a conservative margin to the average value such that

H _(k) =H _(k)−λ_(k) Ĥ _(k)  (5)

where H_(k) is known as the “true” happiness, and λ_(k) is a scalingfactor which controls the level of “conservativeness”. The quantityĤ_(k) is the weighted standard deviation of happiness within cell k, andis then given by

Ĥ _(k)=√{square root over (H _(k) ⁽²⁾−(H _(k) ⁽¹⁾)².)}  (6)

The effect of offsetting the happiness factor in order to increaseconservativeness for power adjustment is shown in FIG. 3. FIG. 3 showsthe probability density function of H_(k). With power managementoperating such that H _(k)−1, the area of Region A in FIG. 3 indicatesthe probability that the true happiness is below unity. By offsettingthe happiness factor by λ_(k)Ĥ_(k), the probability that the truehappiness is below unity reduces from the area of Region A to that ofRegion B.

FIG. 4 illustrates a more general way to increase conservativeness, bydefining H_(k) as the X^(th) percentile of H_(k,i), ∀i. Under thisdefinition, only X % of the happiness would fall below unity as shown inFIG. 4.

FIG. 5 shows a process for setting downlink power, incorporating thetrue happiness factor. This process is repeated periodically.

In step 70, a sub-band index j_(*) is picked, such that D_(j) _(*) (k)is the smallest among all j's, given that D_(j)(k)<0 and P_(k,j)>0.Thus, this step selects the sub-band for which a power decrease wouldhave the most beneficial effect.

The process then passes to step 72, in which the power is reduced in thesub-band index j_(*). Specifically, the power is reduced by a decrementvalue δP from its current value P_(k,j) _(*) , although of course itcannot be reduced below zero. Thus, P_(k,j) _(*) =max (P_(k,j) _(*) −δP,0).

After completing step 72, the process passes to step 74. In step 74, itis determined whether the total transmit power for the cell P_(k) isless than the maximum allowed total power {tilde over (P)}_(k).

If the total transmit power for the cell is less than the maximumallowed total power, then the power can be increased in one of thesub-bands, and this sub-band is selected in step 76. Thus, step 76selects the sub-band for which a power increase would produce thelargest beneficial effect. That is, sub-band j* is picked, such thatD_(j) _(*) (k) is the largest among all j's, where D_(j)(k)>0.

The happiness of the cell is then used to decide whether in fact toincrease the power in that sub-band. Specifically, the process passes tostep 78, in which it is tested whether the cell is happy. This isdetermined by testing whether the true happiness is less than unity,i.e. whether H_(k)<1. If this condition is met, then it is determinedthat the cell is not happy enough, and the process passes to step 80, inwhich the power is increased in the sub-band selected in step 76.Specifically, the power is increased by an increment value δP from itscurrent value P_(k,j*), or by the maximum increment that can be appliedwithout increasing the total power of the cell beyond the maximumallowed total power {tilde over (P)}_(k), if the latter increment issmaller. That is, step 80 sets P_(k,j*)=P_(k,j*)+min (δP, {tilde over(P)}_(k)−P_(k)).

If it is determined in step 78 that the cell is happy enough, i.e.H_(k)≧1, the power is reduced, in order to save energy and increaseefficiency. Specifically, the power is reduced by a decrement value δPfrom its current value P_(k,j*), although of course it cannot be reducedbelow zero. Thus, step 82 sets P_(k,j*)=max (P_(k,j*)−δP, 0).

If it was determined in step 74 that the maximum total power for thecell is already being used, then the power can be increased in onesub-band only if it is also decreased in another sub-band. Therefore, ifit is determined in step 74 that the inequality is not true, the processpasses to step 84, in which sub-bands are selected. Thus, a sub-band j*is selected as the most favourable for a power increase, and a sub-bandj_(*) is selected as the most favourable for a power decrease, on thebasis that D_(j*)(k) is the largest value of D_(j)(k), among all j's,and D_(j) _(*) (k) is the smallest value of D_(j)(k) for differentvalues of j for which P_(k,j)>0.

Having selected in step 84 the sub-band that is now the most favourablefor a power decrease, the process passes to step 86, in which the poweris reduced by a decrement value δP from its current value P_(k,j) _(*) ,although of course it cannot be reduced below zero. Thus, step 86 setsP_(k,j) _(*) =max (P_(k,j) _(*) −δP, 0).

It is then determined whether it is advantageous to increase the powerin one of the sub-bands, by reallocating the power that was removed fromone of the sub-bands in step 86. Specifically, in step 88, it is testedwhether the cell is happy. This is determined by testing whether thetrue happiness is less than unity, i.e. whether H_(k)<1. If thiscondition is met, then it is determined that the cell is not happyenough, and the process passes to step 90, in which the power isincreased in the sub-band selected in step 86, namely the sub-band inwhich the increase in power has the greatest beneficial effect.Specifically, the power is increased by the amount by which the power inthe sub-band j_(*) was decreased in step 86. Thus, the power isincreased by the increment value δP from its current value P_(k,j*), orby the previous power in the sub-band j_(*) if the latter amount issmaller. That is, step 90 sets P_(k,j*)=P_(k,j*)+min (δP, P_(k,j) _(*)).

If it is determined in step 88 that the cell is happy enough, i.e.H_(k)≧1, the power is reduced, in order to save energy and increaseefficiency. Specifically, the power is reduced by a decrement value δPfrom its current value P_(k,j*), although of course it cannot be reducedbelow zero. Thus, step 92 sets P_(k,j*)=max (P_(k,j*)−δP, 0).

Thus, the process tests in steps 78 and 88 whether the true happiness isless than unity, and steps 82 and 92 are able to set lower power valuesthan would otherwise be set, if the true happiness is greater than orequal to than unity.

FIG. 6 illustrates the effect on the achieved utility of choosingdifferent values for the scaling factor λ_(k). Specifically, FIG. 6shows the average utility per cell (in this illustrative embodiment,this is as defined above, i.e. as the sum of the logarithms of theaverage bit rates over all users) as a function of time for λ_(k)=0.01(line 100 in FIG. 6) and λ_(k)=1.20 (line 102 in FIG. 6) at a targettransport block size (TBS) of 70 bytes per Transmission Time Interval(TTI). For comparison purposes, the result for the case without QoSrequirement (line 104 in FIG. 6) is also included. At λ_(k)=0.01, it canbe seen that the average utility tracks the target (line 106 in FIG. 6)reasonably well. As λ_(k) increases to 1.20, the system becomes moreconservative, resulting in an increase in the average utility asexpected, and hence a reduction in the number of users whose achievedbit rate falls below the required rate. In the case when no QoS limit isapplied, the system would use as much power as possible, and the utilityis correspondingly higher.

FIG. 7 illustrates the effect on the average power per cell of choosingdifferent values for the scaling factor λ_(k). Specifically, FIG. 7shows the average power per cell as a function of time for λ_(k)=0.01(line 110 in FIG. 7) and λ_(k)=1.20 (line 112 in FIG. 7). For comparisonpurposes, the result for the case without QoS requirement (line 114 inFIG. 7) is also included. Thus, while the system achieves a higherutility without taking into account the QoS limit, the transmit power isalso higher, as each eNB transmits at its maximum power of 10 mW asshown in FIG. 7. On the other hand, when the happiness factor is appliedwhile taking into account the QoS requirement, significant power savingcan be achieved. In the case where λ_(k)=0.01, the utility reduces byabout 8% compared to the case without the QoS limit, while the transmitpower is lowered by more than 80%. A smaller reduction in utility, butwith a correspondingly smaller reduction in transmit power, can beachieved by setting a higher, more conservative, scaling factor. Thisreduction in transmit power can be attributed not only to the reducedbit rate requirement, but also the lowering of the overall interference.This shows that significant power savings can be achieved.

As mentioned above, the scaling factor λ_(k) controls the“conservativeness” of the utility, in such way that a higher valueimproves the overall utility of the system at the expense of a highertransmit power. Thus, this parameter provides a degree of freedom totune the utility level of the system via the trade-off between utilityand power consumption.

For example, the scaling factor can be adjusted based on the currenttransmit power. If the current transmit power reaches its maximum value,the system performance is not likely to be increasing. On the otherhand, by decreasing λ_(k), a small reduction in the overall utilitymight occur, but there might be a potentially significant reduction inpower. Thus, one alternative to the above algorithms is to reduce λ_(k)by a step Δλ_(k) if the average power P _(k) is above a certainthreshold, and to increase λ_(k) by a step Δλ_(k) if the average poweris below another threshold.

When the scaling factor λ_(k) is high, more power is used to improve theoverall utility within the cell, thereby increasing the level ofdownlink interference for the neighbours. Thus, another alternative tothe above algorithms is to adapt λ_(k) in a cell, based on the level ofdownlink interference observed at the cell. The interference value canbe obtained based on the Evolved UMTS Terrestrial Radio Access (E-UTRA)Carrier Received Signal Strength Indicator (RSSI) using the downlinklisten mode (DLM) or mobile measurements. These measurements can bebased on the time-average RSSI values, or based on the percentile of theRSSI values. The recommendation to lower the λ_(k) value is thentransmitted to the neighbours, for example via a private message in theX2 interface.

As discussed above, the quantity D_(j)(k,m) describes the level ofeffects of utility due to the power change from neighbour m at sub-bandj. Subsequently, the aggregate impact of the change of utility over allneighbours for sub-band j is given by

$\begin{matrix}{{D_{j}(k)} = {\sum\limits_{m}\; {D_{j}\left( {k,m} \right)}}} & (7)\end{matrix}$

The method of computing D_(j)(k) proposed in Stolyar thus involves thecalculation of the rate of change of the utility function with respectto the power. This quantity is then aggregated, as shown by equation(2), and the result is distributed to the neighbours. However, there isno standard interface which allows such a quantity to be passed betweenbase stations (in particular such quantity is not supported by thestandard X2 interface), and so the communication of this result requiresa proprietary interface between base stations. Therefore, as it might beinconvenient or impossible to provide a proprietary interface, and it ismore efficient to use the standard X2 interface if one is available, inorder to provide an algorithm that can be used by base stationsconnected only by the X2 interface, an alternative formulation of theD_(j)(k) value is used.

According to TS36.423, X2 application protocol (X2AP), V8.3.0, 3GPP,2008. 0, a Relative Narrowband Tx Power (RNTP) information element (IE)is included in the Load Information X2 message. For each resource block,the RNTP IE informs the neighbouring cells whether the sending cellpower at such resource block is above (1), or below (0) a certainthreshold (RNTP threshold). In order to be able to use the X2-interface,we need to formulate D_(j)(k,m) in terms of what are available in X2.The reformulated values for D_(j)(k,m) can then be exchanged betweenbase stations.

As one example of such a reformulation, let:

$\begin{matrix}{{D_{j}\left( {k,m} \right)} = \left\{ \begin{matrix}{- {\sum\limits_{i}\; {\frac{G_{i}^{(m)}}{G_{i}^{(k)}}\rho_{j,m}}}} & {m \neq k} \\0 & {m = k}\end{matrix} \right.} & (8)\end{matrix}$

where G_(i) ^((m)) is the path gain between the mobile i (served by cellk) and neighbour m, and ρ_(j,m) is the RNTP for sub-band j.

So, mobile devices can make measurements from the neighbouring cells, inorder to obtain this information, and can report back to the servingbase station. The serving base station can then make the calculationsbased on equation (8).

The path gain G_(i) ^((m)) can be obtained at the mobile device bymeasuring the Reference Signal Reference Power (RSRP) (described in TS36.214, Physical layer; Measurements, V9.2.0, 3GPP, 2010) and thecorresponding transmit power from neighbour m via the neighbour'sbroadcast channel.

More precisely, let the path gain sampled at time t be:

$\begin{matrix}{{g_{i}^{(m)}(t)} = \frac{{RSRP}_{m}(t)}{P_{m}^{ref}}} & (9)\end{matrix}$

where RSRP_(m)(t) is the RSRP from cell m sampled at time t, and P_(m)^(ref) is the reference signal power from the neighbour's broadcastchannel.

As an alternative, g_(i) ^((m))(t) can be defined as g_(i)^((m))(t)=RSRP_(m)(t), as the ratio of the RSRP values would alsoprovide the relative impact of the neighbour base station m with respectto the serving base station.

Note that the RSRP measurements obtained at the mobile or at the basestation (using a Downlink Monitor (DLM) in the vicinity of the basestation) can fluctuate due to channel fading, shadowing, etc. It istypically more representative to take an average over many samples inorder to recover the long-term average of the path gain. Thus, G_(i)^((m))(t) can be obtained as an exponential average: G_(i)^((m))(t)=(1−α)G_(i) ^((m))(t−1)+αg_(i) ^((m))(t) or more simply as ablock average:

${G_{i}^{(m)}(t)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\; {{g_{i}^{(m)}\left( {t - i} \right)}.}}}$

Alternatively, G_(i) ^((m))(t) can be an x-percentile of the samples{g_(i) ^((m))(t), t=t−1, t−2, . . . , t−N}.

The quantity ρ_(j,m) can be a reasonable aggregate of the RNTP valuesfor each resource block within a sub-band. A simple solution is

$\begin{matrix}{{\rho_{j,m} = {\frac{1}{Q}{\sum\limits_{q = 1}^{Q}\; \rho_{j,m}^{(q)}}}},} & (10)\end{matrix}$

where Q is the number of resource blocks per sub-band, and ρ_(j,m)^((q)) is the RNTP for resource block q in sub-band j from neighbour m.Another way to aggregate the per-resource block values into a sub-bandis to take the maximum value among ρ_(j,m) ^((q)), ∀q, for example.

FIG. 8 is an overall flow diagram of the process, which is repeatedperiodically. Note that the quantity D_(j)(k,m) no longer explicitlyrepresents the sensitivity of the utility of cell k at sub-band j withrespect to the power from neighbour m. Rather, it represents theaggregate impact among mobiles in cell k due to cell m if cell k were totransmit at sub-band j. The more negative the quantity is, the moreimpact it has, and, therefore, cell k would further avoid itstransmission at the respective sub-band.

It is important to note that the formulation of D_(j)(k,m) in equation(8) above assumes that the mobiles have the capability of measuring thebroadcast channel, and obtain the transmit power of the neighbour, aswell as the direct measurement of RSRP of the same neighbour. Asimplified way to compute D_(j)(k,m) is given by

$\begin{matrix}{{D_{j}\left( {k,m} \right)} = \left\{ {\begin{matrix}{{- \frac{G^{(m)}}{G_{k}}}\rho_{j,m}} & {m \neq k} \\0 & {m = k}\end{matrix},} \right.} & (11)\end{matrix}$

where G^((m)) is the path gain between the DLM which resides at thevicinity of the base station for cell k and the correspondingtransmitter at the base station in cell m, and G_(k) is some positiveconstant.

In the formulation in equation (11), a larger value of D_(j)(k,m) is avalue that is closer to zero. If the path gain of the neighbour at j islarge, and the neighbour is transmitting at higher power as indicated byρ_(j,m), then the ratio takes on a large value, and the negative sign infront of that would make this quantity more negative, and further awayfrom zero. The more negative this quantity is, the more detrimental thissub-band j would be for transmission. Thus, the sensitivity andtherefore the risk are higher if the serving base station were totransmit at sub-band j

If no mobile reporting information is available, allowing the path gainbetween the served mobile and the neighbours to be calculated, theserving base station can still rely on its Downlink Monitor (DLM), whereit detects signals transmitted by neighbouring base stations on systemdownlink frequencies, to do the estimation of the path gain (between itsDLM and the neighbour). In other words, the DLM acts like a user for thepurpose of path gain estimation. Of course, this would not be asrepresentative as obtaining information from the mobile users, as themobile users are in different locations within the cell.

Finally, if no DLM information is available, then the base station wouldhave to rely on the information that the X2 interface provides, namelythe ρ_(j,m) value, and so D_(j)(k,m) could be defined as:

$\begin{matrix}{{D_{j}\left( {k,m} \right)} = \left\{ {\begin{matrix}{- \rho_{j,m}} & {m \neq k} \\0 & {m = k}\end{matrix}.} \right.} & (12)\end{matrix}$

Thus, the X2-compliant version of the algorithm reformulates D_(j)(k) insuch a way that it makes use of data that can be made available in theX2 interface between two eNBs. As examples, D_(j)(k) can be redefined asshown in equations (8), (11), or (12) above.

As a result of the redefinition, some modifications of the originalalgorithm are made in order to make the algorithm more stable androbust.

Thus, in FIG. 8, in step 120, a sub-band index j_(*) is picked, suchthat D_(j) _(*) (k) is the smallest among all j's, given that D_(j)(k)<0and P_(k,j)>0. Thus, this step selects the sub-band for which a powerincrease would have the lowest, or least beneficial, effect on the cellperformance, and it is this sub-band whose power might be reduced later.

In step 122, a sub-band index j* is picked, the intention being toselect the sub-band for which a power increase would have the greatest,or most beneficial, effect on the cell performance. As shown byequations (7) and (11), in the best sub-band D_(j)(k) would have a valueof zero, and it is possible that there would be multiple sub-bands whichwould satisfy this criterion. In order to avoid the possibility that thepower is increased in only one sub-band, the sub-band in which powermight be increased later is chosen randomly from a set of sub-bandshaving D_(j)(k)=0. In this way, potentially more sub-bands can take onnon-zero power, and the sub-band utilization increases.

In step 124, it is tested whether D_(j) _(*) (k)<0. As the sub-bandindex j has been picked such that D_(j) _(*) (k) is the smallest amongall j's, step 124 tests in effect whether there is any sub-band having anegative value for D_(j) _(*) (k). That is, step 124 tests whether thereexists any sub-band for which a power increase would have anon-beneficial effect.

In step 124, it may also be tested whether the cell is happy. This isdetermined by testing whether the true happiness H_(k) is greater thanthe product of a Quality of Service (QoS) requirement η_(k) and ahysteresis factor ξ_(k), i.e. it is tested whether H_(k)>η_(k)ξ_(k). Thevalue of the QoS requirement may, for example, be set to a value of 1.

If it is found in step 124 that D_(j) _(*) (k)<0 and, where it is alsotested whether the cell is happy, also that H_(k)>η_(k)ξ_(k), theprocess passes to step 126, in which the power is reduced in thesub-band index j_(*). Specifically, the power is reduced by a decrementvalue δP from its current value P_(k,j) _(*) , although of course itcannot be reduced below zero.

After completing step 126, or if it is found in step 124 that there isno sub-band for which a power increase would have a non-beneficialeffect and/or that the true happiness H_(k) is not greater than theproduct of a Quality of Service (QoS) requirement η_(k) and a hysteresisfactor ξ_(k), the process passes to step 128.

In step 128, it is determined whether the total transmit power for thecell P_(k) is less than the maximum allowed total power {tilde over(P)}_(k), and simultaneously whether it is beneficial for the power tobe increased in the sub-band selected in step 122, i.e. whether D_(j)_(*) (k)=0.

If both of these conditions are met, the process passes to step 130, inwhich it is tested whether the cell is happy. This is determined bytesting whether the true happiness is less than the QoS requirementη_(k), i.e. whether H_(k)<η_(k). Where the QoS requirement is set at avalue of 1, this is determined by testing whether the true happiness isless than unity, i.e. whether H_(k)<1. If this condition is met, then itis determined that the cell is not happy enough, and the process passesto step 132, in which the power is increased in the sub-band selected instep 122. Specifically, the power is increased by an increment value δPfrom its current value P_(k,j*), or by the maximum increment that can beapplied without increasing the total power of the cell beyond themaximum allowed total power {tilde over (P)}_(k), if the latterincrement is smaller. That is, step 132 sets P_(k,j*)=P_(k,j*)+min (δP,{tilde over (P)}_(k)−P_(k)).

If it is determined in step 130 that the cell is happy enough, i.e. thatH_(k)≧η_(k) (or, where the QoS requirement is set at a value of 1, thatH_(k)≧1), the process passes to step 133, in which it is determinedwhether the true happiness H_(k) is greater than the product of the QoSrequirement η_(k) and the hysteresis factor ξ_(k), i.e. it is determinedwhether H_(k)>η_(k)ξ_(k). Where the QoS requirement is set at a value of1, it is actually determined whether the true happiness H_(k) is greaterthan the hysteresis factor ξ_(k), i.e. it is determined whetherH_(k)>ξ_(k).

If it is determined in step 133 that the true happiness is more thansufficient, i.e. that H_(k)>η_(k)ξ_(k) (or, where the QoS requirement isset at a value of 1, that H_(k)>ξ_(k)), the power is reduced, in orderto save energy and increase efficiency. Specifically, the power isreduced by a decrement value δP from its current value P_(k,j*),although of course it cannot be reduced below zero. Thus, step 134 setsP_(k,j*)=max (P_(k,j*)−δP, 0).

If it was determined in step 128 that the maximum total power for thecell is already being used, or that it is not beneficial for the bestsub-band to increase power, the process passes to step 136, in which itis determined whether the total transmit power for the cell P_(k) isequal to the maximum allowed total power {tilde over (P)}_(k), andsimultaneously whether it is beneficial for the power to be increased inthe sub-band selected in step 122, i.e. whether D_(j*)(k)=0. If theseconditions are not met, the algorithm stops and waits until the nextexecution begins. However, if these conditions are met, it suggests thatit is still worthwhile to do further power adjustments.

As the total transmit power for the cell is already at the maximumallowed total power, the adjustments require a sub-band in which thepower can be decreased. Thus, it is tested in step 138 whether D_(j)_(*) (k)=0, i.e. whether the power can beneficially be increased even inthe sub-band with the lowest value of D_(j) _(*) (k). If this conditionis met, the process passes to step 140.

In step 140, a new sub-band is selected randomly from the set ofsub-bands having D_(j)(k)=0, and the process then passes to step 142.

Alternatively, if it found in step 138 that the sub-band with the lowestvalue of D_(j) _(*) (k) has D_(j) _(*) (k)≠0, or more specifically hasD_(j) _(*) (k)<0, i.e. that the power can beneficially be decreased inthis sub-band, the process passes directly to step 142.

In step 142, the power is decreased in the sub-band found in step 138 tohave the lowest negative value of D_(j) _(*) (k), or the sub-bandselected in step 140. Specifically, the power is reduced by a decrementvalue δP from its current value P_(k,j) _(*) , although of course itcannot be reduced below zero. Thus, step 142 sets P_(k,j) _(*) =max(P_(k,j) _(*) −δP, 0).

It is then determined whether it is advantageous to increase the powerin one of the sub-bands, by reallocating the power that was removed fromone of the sub-bands in step 142. Specifically, in step 144, it istested whether the cell is happy. This is determined by testing whetherthe true happiness is less than unity, i.e. whether H_(k)<1. If thiscondition is met, then it is determined that the cell is not happyenough, and the process passes to step 146, in which the power isincreased in the sub-band selected in step 122, namely the sub-band inwhich the increase in power has the greatest beneficial effect.Specifically, the power is increased by the amount by which the power inthe sub-band j_(*) was decreased in step 142. Thus, the power isincreased by the increment value δP from its current value P_(k,j*), orby the previous power in the sub-band j_(*) if the latter amount issmaller. That is, step 146 sets P_(k,j*)=P_(k,j*)+min (δP, P_(k,j) _(*)).

If it is determined in step 144 that the cell is happy enough, i.e. thatH_(k)≧η_(k) (or, where the QoS requirement is set at a value of 1, thatH_(k)≧1), the process passes to step 147, in which it is determinedwhether the true happiness H_(k) is greater than the product of the QoSrequirement η_(k) and the hysteresis factor ξ_(k), i.e. it is determinedwhether H_(k)>η_(k)ξ_(k). Where the QoS requirement is set at a value of1, it is actually determined whether the true happiness H_(k) is greaterthan the hysteresis factor ξ_(k), i.e. it is determined whetherH_(k)>ξ_(k).

If it is determined in step 147 that the true happiness is more thansufficient, i.e. that H_(k)>η_(k)ξ_(k) (or, where the QoS requirement isset at a value of 1, that H_(k)>ξ_(k)),the power is reduced, in order tosave energy and increase efficiency. Specifically, the power is reducedby a decrement value δP from its current value P_(k,j*), although ofcourse it cannot be reduced below zero. Thus, step 148 sets P_(k,j*)=max(P_(k,j*)−δP, 0).

Thus, the combined effect of steps 140, 142 and 146 is to reduce thepower in a good sub-band, and increase it in another good sub-band. Thiscreates an opportunity for the system to redistribute power amongsub-bands, and to randomize and diversify the power allocated to thesub-bands in order to avoid falling into local maxima.

One alternative to the algorithm shown in FIG. 8 is to replace decisionblocks 128 and 136 by a single decision as to whether the total transmitpower for the cell is less than the maximum allowed total power cell,i.e. whether P_(k)<{tilde over (P)}_(k). In this way, the power increasedoes not necessarily have to wait until a sub-band is completelyinterference free, and the base station may increase the power at thesub-band with the least interference.

Another alternative, which provides a slight generalization of thealgorithm in FIG. 8 is to replace the selection in step 120 by a randomselection of j_(*). That is, j_(*) can be randomly selected from the setΩ_(k), where Ω_(k)={(1), (2), . . . , (M_(k))}, with 1≦M_(k)≦J and (j)being the index corresponding to the i-th smallest value of D_(j)(k),i.e. D₍₁₎(k)≦D₍₂₎(k)≦ . . . ≦D_((J))(k). When M_(k)=1, this reduces tothe original step 120 in FIG. 8. The purpose of this generalization isto randomize and diversify the selection of j_(*) in order to furtherimprove the optimization results.

FIG. 9 shows the average utility per cell as a function of time, whenchoosing different values for the scaling factor λ_(k)=0.01 (line 160 inFIG. 9) and λ_(k)=1.20 (line 162 in FIG. 9) at a target transport blocksize (TBS) of 90 bytes per Transmission Time Interval (TTI). Forcomparison purposes, the result for the case without QoS requirement(line 164 in FIG. 9) is also included. Similarly to FIG. 6 above, theaverage utility per cell converges to the target (line 166 in FIG. 9),provided that it is feasible. However, the convergent time is slightlylonger, especially for the case of λ_(k)=0.01.

FIG. 10 illustrates the effect on the average power per cell of choosingdifferent values for the scaling factor λ_(k). Specifically, FIG. 10shows the average power per cell as a function of time for λ_(k)=0.01(line 170 in FIG. 10) and λ_(k)=1.20 (line 172 in FIG. 10). Forcomparison purposes, the result for the case without QoS requirement(line 174 in FIG. 10) is also included. Thus, the power efficiency isagain very high for a reasonable bit rate target.

As described above, the scaling factor can be adjusted based on thecurrent transmit power, or based on the observed level of downlinkinterference.

It can be seen that the gap between the aggregate QoS limit among thesupporting mobiles and the cell capacity defines the energy efficiencyof the cell. In other words, when the aggregate QoS limit is higher thanthe cell capacity, full power would be used, and no power saving ispossible. However, by bringing the QoS limit down to and slightly belowthe cell capacity, power saving starts to become possible.

One further proposal to achieve energy saving is to adaptively lower theQoS limit by observing the cell throughput dynamics.

In order to obtain the sensitivity D_(j)(k,m) as described above, weneed to compute the derivative of the cell utility with respect to thetransmit power in cell m at sub-band j. Typically, the cell utility isrelated to the spectral efficiency of the sub-bands. For example, let

$\begin{matrix}\begin{matrix}{{D_{j}\left( {m,k} \right)} = \frac{\partial U_{k}}{\partial P_{m,j}}} \\{\approx {\sum\limits_{i \in \Omega_{k}}\; {f\left( \frac{\partial{\omega \left( \gamma_{i,j}^{(k)} \right)}}{\partial P_{m,j}} \right)}}} \\{= {\sum\limits_{i \in \Omega_{k}}\; {f\left( {\frac{\partial{\omega \left( \gamma_{i,j}^{(k)} \right)}}{\partial\gamma_{i,j}^{(k)}} \cdot \frac{\partial\gamma_{i,j}^{k}}{\partial P_{m,j}}} \right)}}}\end{matrix} & (13)\end{matrix}$

where Ω_(k) is the set of user indices in cell k, γ_(i,j) ^((k)) is theSignal-to-Interference and Noise Ratio (SINR) of user i in cell k atsub-band j, and ω is the spectral efficiency which is a function ofγ_(i,j) ^((k)). The term f(.) is a pre-defined function which definesD_(j)(k,m), and, therefore, is known to the base station. The quantity∂γ_(i,j) ^((k))/∂P_(m,j) is relatively straight-forward, as γ_(i,j)^((k)) is a well-known function of P_(m,j). The main issue is thequantity ∂ω(γ_(i,j) ^((k)))/∂γ_(i,j) ^((k)), which depends on the natureof ω, and is not known exactly in practice. Typically, it is oftenassumed that

$\begin{matrix}{{{\omega (x)} = {\log_{2}\left( {1 + \frac{x}{\hat{\Gamma}}} \right)}},} & (14)\end{matrix}$

where {circumflex over (Γ)} is a fixed value often known as the“capacity-gap” constant, as it determines how far it is from the actualchannel capacity. For simplicity, {circumflex over (Γ)}=1 is assumed inthe prior art document R. Kwan, C. Leung, “A Survey of Scheduling andInterference Mitigation in LTE”, Volume 2010, Article ID 273486, while{circumflex over (Γ)}=log (5ε_(b))/1.5, (where ε_(b) is the bit errorrate) is assumed in other prior art documents, such as A. J. Goldsmith,S-G Chua, “Variable-Rate Variable-Power MQAM for Fading Channels”, IEEEtrans. on Comm. Vol. 45, no. 10, October 1997; G. Piro, N. Baldo. M.Miozzo, “An LTE module for the ns-3 network simulator”, in Proc. of Wns32011 (in conjunction with SimuTOOLS 2011), March 2011, Barcelona(Spain); and H. Seo, B. G. Lee. “A proportional-fair power allocationscheme for fair and efficient multiuser OFDM systems”, in Proc. of IEEEGLOBECOM, December 2004. Dallas (USA).

It is important to note that the analytical relationship described inequation (14) above is only theoretical, as the actual SINR is not knownto the base station. According to 3GPP TS 36.213, Physical layerprocedures, Release 9, v9.3.0, the mobile measures the downlink channelquality in the form of an SINR, and packages such a quantity in a formof an index known as the Channel Quality Indicator (CQI). It is the CQIthat is available to the receiving base station.

Also, equation (14) defines a static relationship which, even if it is agood approximation in a certain environment, may not be as accurate inanother. In practice, the spectral efficiency vs channel qualityrelationship dependency would likely be different due to vendor-specificimplementation of the receiver structures. Thus, a more robust way ofrelating ω to γ_(i,j) ^((k)) would be extremely useful.

According to 3GPP TS 36.213, Physical layer procedures, Release 9,v9.3.0, there is a definite relationship between the spectral efficiencyand the reported CQI from the mobile. In other words, once the CQI isknown, the base station can obtain the spectral efficiency correspondingto each CQI report via a look-up table. While an explicit analyticalrelationship between spectral efficiency and CQI is not given, wepropose to approximate the spectral efficiency fairly reasonably as apower function of the CQI:

ω=aq ^(b)  (15)

where q is the CQI, a=0.077, and b=1.586.

While the relationship between spectral efficiency and CQI is fixed, theway CQI is measured is not standardized, although it most likely dependson the measured SINR. The way SINR is measured is vendor-specific, anddepends on a number of factors, including the implementation of receiveralgorithms involved, the accuracy of the estimation, etc. However, inpractice, the CQI is designed in such a way that it is fairly linear asa function of the SINR in dB. Each point at a given CQI value in such alinear relationship lies in a similar distance from its neighbour.Despite the possible diversity of vendor-specific implementations, suchrelationships are not expected to deviate much from each other, as thereare only a limited number of reasonable ways of designing a goodreceiver given a standardized algorithm at the transmitter side. A goodexample of the relationship between CQI and SINR can be found in theprior art document C. Mehlführer, M. Wrulich, J. C. Ikuno, D. Bosanska,M. Rupp, “Simulating the Long Term Evolution Physical Layer”, Proc. of17^(th) European Signal Processing Conference (EUSIPCO), 2009.

An empirical approximation of such a relationship is:

q=cγ _(dB) +d  (16)

where γ_(dB) is the SINR expressed in decibels (and, henceγ_(dB)=10.log₁₀γ, where γ is the SINR), c=0.5, and d=4.4. Thus, thespectral efficiency as a function of the SINR is then given by

ω=a(c′ log₁₀(γ)+d)^(b)  (17)

where c′=10c.

As mentioned earlier, the CQI vs SINR curve is not standardized, andslight implementation differences may exist between vendors. Despitethis, it is possible to compensate for such differences by introducingan offset Δd to equation (17) such that

ω=a(c′ log₁₀(γ)+d+Δd)^(b).  (18)

Equation (18) lends itself to a simple form which is continuouslydifferentiable, and the derivative itself is relatively simple.

FIG. 11 shows the adjustment of the relationship between spectralefficiency ω and SINR via the CQI offset Δd. Specifically, introducing apositive offset Δd shifts the CQI against SINR relationship from thatindicated by line 180 to that indicated by line 182, and so means that,for a given measured SINR value, a higher value of CQI is obtained. Thisthen means that a point higher up the spectral efficiency against CQIcurve 184 is selected, and hence a higher value for the spectralefficiency ω. Note that, from the point of view of computing D_(j)(m,k),the offset Δd does not necessarily need to be quantized, as the main aimis to obtain an analytical approximation to the spectral efficiency ω sothat the derivative with respect to the SINR can be computed.

FIG. 12 shows the effect of CQI adjustment by means of offset Δd. As anexample, FIG. 12(a) shows the effect of introducing an offset of Δd=−2,namely that the original CQI line 190 (based on the results obtained inthe prior art document C. Mehlführer, M. Wrulich, J. C. Ikuno, D.Bosanska, M. Rupp, “Simulating the Long Term Evolution Physical Layer”,Proc. of 17^(th) European Signal Processing Conference (EUSIPCO), 2009)is shifted vertically downward to the line 192. That is a lower CQIvalue is obtained for any given SINR value.

FIG. 12(b) then shows that, by shifting of the CQI value, the originalspectral efficiency curve produced by Vienna University of Technology(VUT) in the Mehlführer et al prior art document (line 194 in FIG.12(b)) is shifted to produce lower values for the spectral efficiency,and the resulting curve (line 196 in FIG. 12(b)) matches the spectralefficiency curve (line 198 in FIG. 12(b)) produced independently byCentre Tecnològic de Telecommunicacions de Catalunya (CTTC) based on theassumption in the prior art document G. Piro, N. Baldo. M. Miozzo, “AnLTE module for the ns-3 network simulator”, in Proc. of Wns3 2011 (inconjunction with SimuTOOLS 2011), March 2011, Barcelona (Spain).

One way to determine the value of Δd is via the Hybrid ARQ feedback. Ifthe ratio of the number of Negative ACKnowledgement (NACK) messages tothe total number of transmissions (including retransmissions) is largerthan a certain threshold over a certain period of time, Δd isdecremented by one. On the other hand, if this ratio is lower than acertain threshold over a certain time period, Δd is incremented by one.

Thus, if there are a high proportion of NACK messages, this means thatthe channel quality is lower than previously thought, and so the offsetvalue is decremented, which means that the derived value of CQI isreduced. A lower value of CQI means it is more “conservative”, and lesserror-prone.

Thus, this provides a way to obtain an empirical, analytically simplerelationship between the spectral efficiency and the SINR. This isimportant as CQI is the only information available to the base stationaccording to the standard. Such a relationship can then be used toobtain the sensitivity function for the above-described power managementmechanism. This generic relationship provides a way to adapt itself tosome true underlying relationship via a simple adjustment of parameter.

Hybriad ARQ feedback can then be used to adjust the parameter such thatthe estimated relationship better matches the true underlyingrelationship. As alternatives to HARQ feedback, it is possible to usethe difference between average block error rate and the respectivetarget value, i.e. X=avg BLER−target BLER. If X is above zero (or, evenbetter, a small positive threshold) over a period of time T, the offsetis reduced by one unit. On the other hand, if X is below zero (or, asmall negative threshold) over a period of time T, the offset isincreased by one unit.

Note that the above methods require a dedicated interface between twonodes, so that the nodes can communicate the information required forsetting power values as discussed above. FIG. 13 illustrates a possibledeployment, with a femto layer 220 comprising multiple HeNB's 222 a, 222b, . . . , 222 k, and a macro layer 224 comprising multiple eNB's 226 a,226 b, . . . , 226 k. Within the femto layer 220, it may be reasonableto assume that all HeNBs can communicate with each other via the X2interface. This is especially like to happen in what is known as the“enterprise” environment, where all HeNBs are likely from the samevendor. In the macro layer 224, all eNBs are also expected to be able tocommunicate with each other via the X2 interface. However, it may not bealways possible to have an X2 interface between the femto layer 220 andmacro layer 224.

Another relevant aspect of the deployment, in a network of the typeshown in FIG. 13, is the way that the spectrum is overlapped between themacro and femto layers.

FIG. 14 shows three different possibilities, illustrating schematicallyhow the available frequency band is divided between the macro and femtolayers.

A first possibility, case A, is that sub-bands 230 are allocated to themacro layer and sub-bands 232 are allocated to the femto layer, so thereis no frequency overlap between the two layers. Thus, there is no needto perform interference mitigation between the two layers, as thefrequency bands involved are not co-channel.

A second possibility, case B, is that sub-bands 234 are allocated to themacro layer and sub-bands 236 are allocated to the femto layer, so thatthe frequency band of the femto layer is completely overlapped by thatof the macro layer. Thus, while the non-overlapped region of the macrolayer is not affected, the impact on the overlapped region couldpotentially be significant. In this case, interference managementbecomes very useful.

The intermediate possibility, case C, is that sub-bands 238 areallocated to the macro layer and sub-bands 240 are allocated to thefemto layer, and there is a partial overlap between the macro and femtolayers. The schedulers of the base stations in the respective layers areexpected to select sub-bands automatically so as to avoid the inter-cellinterference, and the relationship between sub-bands in the two layerscan be mapped using their respective Evolved UMTS Terrestrial RadioAccess (E-UTRA) Absolute Radio Frequency Channel Numbers (EARFCN) andbandwidths, which can be exchanged via the X2 interface. However, byincorporating the power management whereby lower power is allocated tosub-bands of higher interference and vice versa, higher performance canstill be expected.

Below are set out the possible deployment scenarios allowingcommunication between the various base stations, in the case of thefirst method described above and shown in FIG. 5, in which powermanagement relies on the setting of the power values in accordance withthe calculated happiness values, requiring a proprietary interfacebetween base stations, and in the case of the second method describedabove and shown in FIG. 8, in which power management depends onquantities that can be transmitted over the standard X2 interface.

Base Stations in Femto Layer Only Method Requiring Proprietary InterfaceBetween Base Stations

This is applicable when the HeNBs within a geographic region belong tothe same vendor or vendors with a certain special arrangement. This islikely to happen in an “enterprise” environment, in which femtocellscollectively share a space, where mobile users are expected to roamfreely. In this case, it is possible to define a proprietary message asthe “private message” over the X2.

Method Able to Use X2 Interface

In this scenario, HeNBs can use a standard X2 interface for the purposeof power adaptation. The standard X2-based version does not require theuse of private message in the X2 interface. It is not uncommon that theHeNBs in the service area would belong to the same vendor (or differentvendors sharing a certain arrangement). However, if two base stations donot belong to the same vendor, the HeNB implementing the algorithm canstill benefit from the standard message from its neighbour. Thus, thissolution is less sensitive to issues of compatibility among basestations, as long as they share the standard X2 interface.

Base Stations in Macro Layer Only Method Requiring Proprietary InterfaceBetween Base Stations

The neighbouring macro base stations may come from different vendors,but this method would only be applicable in the case of base stationsfrom the same vendor.

Method Able to Use X2 Interface

This solution does not require a proprietary interface. Therefore, as inthe case above where the base stations are in the femto layer only, theX2 interface can be used without requiring the use of a private message.

Base Stations in Femto and Macro Layers, and X2 Interface AvailableBetween them

Method Requiring Proprietary Interface Between Base Stations

Due to the expectation that a large number of femto cells reside under asingle macro area, it is likely to be more convenient for each HeNB toperform power adaptation than for the macrolayer base station to attemptto set a power that is appropriate for every femtocell. If only theHeNBs are doing the adaptation, there is no need for the power settingalgorithm to run at the macro layer base station (at least not to adaptto the power levels in the femto layer). Thus, there is no vendorcompatibility issue for the macro layer base stations.

Method Able to Use X2 Interface

Again, each HeNB can perform power adaptation, and there is no need forthe power setting algorithm to run at the macro layer base station.

The method shown in, and described with reference to, FIG. 8 applies,using the available X2 interface between the macro and femto layers. Therequired information can be embedded in the Relative Narrowband Tx Power(RNTP) information element (IE) in the Load Information X2 message. Foreach resource block, the RNTP IE informs the neighbouring cells whetherthe sending cell power at such resource block is above (1), or below (0)a certain threshold (RNTP threshold), which is another X2 parameter inthe 3GPP specification. Depending on the flavour of the algorithm,mobile measurements may be required to compute the path gain relative tothe base station. This can be achieved by comparing the mobile downlinkRSRP measurement with the Reference Signal Transmit Power of the systeminformation block (SIB) from the broadcast channel of the neighbourcell. If proprietary information is needed, the Private Message in theX2 interface can be used.

Base Stations in Femto and Macro Layers, and No X2 Interface AvailableBetween them

When no X2 interface is available, it is difficult to estimate theeffect of the interference due to a specific neighbouring macro on afrequency-unit by frequency-unit basis. Thus, the effect of inter-cellinterference would have to be estimated indirectly.

For example, one way to estimate the inter-cell interference without theuse of an X2 interface is to configure and use periodic mobile CQImeasurements across the entire bandwidth.

Firstly, the base station collects these CQI measurements from allcamped mobiles. These CQI measurements are considered instantaneous on asub-frame level, and so, to estimate the inter-cell interference overthe long term, the base station then performs an averaging of thesemeasurements, which can for example be based on an exponential averageor block average, etc.

Since the mobiles are at different geographic locations, their pathgains relative to the respective base stations are different. Thus, theaverage CQI measurements from each mobile are then normalized withrespect to its respective mean value.

The serving base station then gathers the normalized average CQImeasurements from all mobiles belonging to it, and does an averaging ofCQI among all mobiles for each sub-band across the entire bandwidth,resulting in a vector of cell-wise normalized average CQI measurements φ_(k)=(φ_(k,1), φ_(k,2), . . . , φ_(k,j), . . . , φ_(k,J)), where jcorresponds to the index of a sub-band.

For each entry j of {circumflex over (φ)}_(k) that is below a certainthreshold {tilde over (φ)}_(k), the quantity D_(j)(k) can be set to anegative real value. For example, D_(j)(k) can be: (a) a fixed negativereal value; (b) a value picked from a uniform distribution U(−a, −b),where a and b are some positive real values; (c) the valueφ_(k,j)−{tilde over (φ)}_(k); (d) the negative of the largest sum of thepath gain ratio between a neighbour relative to all mobiles attached tothe serving base station (e.g. similar to equation (8) above); or (e) aversion of (d) which involves only the downlink listen mode (DLM),instead of relying on mobile measurements (i.e. similar to equation (11)above).

Once this is done, the algorithm shown in FIG. 8 can then be applied.

It should be noted that frequency selectivity may affect the accuracy ofthe above estimation. That is, the wireless channel can be expected tovary to some extent across the frequency band. Thus, it is expected thatthe estimation will typically be more accurate in a femtocellenvironment, as the delay spread is typically smaller. However, themethod of estimation is not limited to the femtocell environment.

For the case when X2 is not present between the macro and femto layers,but is present within the femto layer, the set of sub-band indices forwhich D_(j)(k) is set should be the union between the set obtained fromthe X2 interface and that using mobile measurements. The value ofD_(j)(k) can for example be obtained using the path gain measurements asset out in options (d) or (e) above, or variations thereof.

It was discussed above that a “happiness factor” can be defined as theaverage bit rate achieved by a user divided by the bit rate requirement,{tilde over (R)}_(k,i). If this bit rate requirement is very highrelative to the capacity of the system to handle such a requirement, thesystem would inevitably attempt to use as much power as possible tofulfil the requirement.

FIG. 15 shows how the average utility function U_(k) and the averagepower P_(k) vary with the bit rate requirement, per mobile, i.e.{circumflex over (R)}_(k,i). When the “capacity” C_(k,sys) of the systemis below the requirement, there is very little gain in using the fullpower as the performance itself is limited by the inherent limit of thesystem. Here, the term “capacity” is defined loosely as the maximumperformance that the system can achieve given the bandwidth, thelocations of the mobiles, etc. On the other hand, as the bit raterequirement approaches and goes slightly below the system capacity, theroom for power saving starts to appear, and the power efficiency startsto improve. As the required bit rate reduces below the system capacity,it becomes possible for the system to reduce the transmit power at theexpense of a small bit rate degradation. However, due to the reductionof inter-cell interference, the reduction of the bit rate due to thelowering of power can then be compensated by the increase in the SINR.Also, the impact of bit rate reduction is further absorbed by thelogarithmic relationship of the utility with respect to the bit rate.

FIG. 16 shows the relationship between the average utility functionU_(k) and the average power P_(k) , with points on the line 250representing the relationship for different values of the bit raterequirement per mobile, i.e. {tilde over (R)}_(k i). As the required bitrate reduces, the state of the system moves towards the left from pointA. It can therefore be seen that the bit rate requirement {tilde over(R)}_(k,i) can be set to a value (for example in the region 252 on theline 250) that achieves significant power savings, compared with thehighest power requirements, but without incurring large penalties interms of the reduction in utility.

Typically, the required bit rate is controlled by the higher layers ofthe network. However, one possibility is for the base station to set thebit rate requirements to lower values as follows:

Firstly, take N consecutive samples of the happiness H_(k,i). IfH_(k,i)<1 occurs for at least N′ (where N′≦N) consecutive samples, andthe system is transmitting at full power, {tilde over (R)}_(k,i) isreduced by a step value Δ{tilde over (R)}_(k i). This adjustment processtakes places very slowly, because the values of N and N′ are relativelylarge compared to the frequency at which the power setting algorithm isinvoked.

This can be repeated until {tilde over (R)}_(k,i) has been reduced tothe lowest tolerable value, or until the reduction in the required bitrate means that the utility is decreasing faster than the average power.So, for example, it can be that the process will repeat itself until 1)the rate of change of the average cell utility with respect to theaverage cell power (the derivative for short) is above a certainthreshold or 2) the average cell utility is below a certain utilitythreshold, or 3) a sub-set of users' utilities are above a certainthreshold. As shown in FIG. 16, the derivative is positive. As the bitrate requirement reduces to a certain level, the value of the derivativestarts to increase very rapidly. The system therefore keeps track ofsuch derivative as the bit rate requirement is reduced and, as condition1), 2), or 3) is met, the reduction of the bit rate requirement stops.

A minimum tolerable bit rate can be associated with each bit raterequirement set by a mobile. As one example, this lowest tolerable valuemight be set to a predetermined fraction of the initial bit raterequirement. The predetermined fraction might be set to be a constantvalue, such as ½ or ¾. Alternatively, the predetermined value might beset based on the traffic type. Thus, the predetermined value might beset to ½ for certain sorts of traffic and to ¾ for certain other sortsof traffic. The lowest tolerable value should always be set such that itprotects user i from service shut-down.

As described above, the happiness of a user is defined as the averagebit rate divided by the bit rate requirement for the user. Thus, as thebit rate requirement is reduced, the user would appear to be more happy.When the user's happiness improves, there is a less frequent need forthe system to increase the power during the power adaptation. Thiscauses the average power to reduce. As the average power reduces, andthe bit rate requirement reduces, the average bit rate of the userreduces. Typically, the utility function U is a function of the bitrate. As the average user bit rate decreases, the corresponding utilitydecreases. However, reducing the bit rate requirement of unhappy users(provided that the bit rate requirement is still above the minimumtolerable bit rate), can reduce the overall average power of the system.

Load computation is an important aspect of LTE, and is relevant in thecontext of admission control, congestion control, and load balancing. Aproper quantification of cell load is needed in order to determinewhether a cell can admit new bearers. When the cell is highly loaded,further entry of radio bearers may be prevented in order to maintain thecall quality of the existing bearers. Once admitted into the system, thecell load can still fluctuate due to the channel quality variations as aresult of channel fading and mobility, etc. Thus, the system would needto cope with such load fluctuation, and some existing bearers may needto be dropped if necessary.

The simplest way to compute the cell load is to compute the averagenumber of resource blocks used relative to the total number of resourceblocks of the bandwidth. One drawback of this approach is that it tendsto over-estimate the load, especially in the presence of best-efforttraffic, and thereby potentially causes inefficient utilization ofresources. A more sophisticated way to define cell load for LTE has beenproposed in R. Kwan, R. Arnott, et. al. “On Radio Admission Control forLTE Systems”, proc. of IEEE VTC-fall, 2010. To compute the cell load,the required number of resource blocks per bearer is obtained, based onthe ratio of the required bit rate and the spectral efficiency perresource block of the user. This quantity is then normalized by thetotal number of resource blocks in the system bandwidth, and summed overall active bearers in the system.

However, this approach assumes a constant power spectral density acrossthe bandwidth. This assumption is valid when frequency-selective powercontrol is not used. However, in the presence of power control acrossthe bandwidth, i.e. each sub-band can potentially take on a differentpower level, such an approach would potentially underestimate the load,because power is non-uniformly distributed across the sub-bands, therebyreducing the usability of some sub-bands.

In order to overcome this problem, the load can be defined as:

$\begin{matrix}{\rho_{k} = {\sum\limits_{i}\; {\frac{{\overset{\sim}{R}}_{k,i}}{{\overset{\_}{R}}_{k,i}}\frac{{\overset{\_}{P}}_{k,i}}{{\overset{\sim}{P}}_{k}}}}} & (19)\end{matrix}$

where {tilde over (R)}_(k,i) and R _(k,i) are the required and averagebit rate for user i in cell k respectively, and P _(k,i) and {tilde over(P)}_(k) are the average power for user i in cell k and the maximumdownlink power limit for cell k respectively. The quantity μ_(k,i)=R_(k,i)/P _(k,i) can be interpreted as the rate per unit power, whichquantifies the power efficiency of the user. Thus, the quantity {tildeover (R)}_(k,i)/μ_(k,i) refers to the power potentially required toachieve the required bit rate. Subsequently, the required powernormalized by the total power gives the relative required powercontribution of the user within the system.

Note that it is possible for a user to have multiple bearers. In thiscase, it is more useful to define i as the index of the bearer in thesystem. Also, in practice, it is possible for a user or a bearer toachieve a very low bit rate, and thereby causing a high loadfluctuation. To overcome this, an alternative version of equation (19)is given by

$\begin{matrix}{{\rho_{k} = {\sum\limits_{i}\; {{\min \left( {C_{i},\; \frac{{\overset{\sim}{R}}_{k,i}}{{\overset{\_}{R}}_{k,i}}} \right)}\frac{{\overset{\_}{P}}_{k,i}}{{\overset{\sim}{P}}_{k}}}}},} & (20)\end{matrix}$

where a positive constant C_(i) is used to put an upper limit on the bitrate ratio, and reduce potential instability.

There is thus described a method of deploying femtocells that allowspower setting to take account of the user requirements.

1-47. (canceled)
 48. A method comprising: determining, at a first basestation, sensitivity of a utility function of a cell served by the firstbase station to changes in transmission powers allocated to one or moresub-bands by at least one other base station that neighbors the firstbase station; and transmitting information from the first base stationto the at least one other base station, wherein the informationcomprises sensitivity information for the utility function for each ofthe one or more sub-bands and wherein the information is associated witha Relative Narrowband Transmit Power of the cell in each of one or moresub-bands.
 49. The method of claim 48, wherein the sensitivity of theutility function is determined based on path gains between the firstbase station and transmitters of the at least one other base station.50. The method of claim 48, wherein the sensitivity of the utilityfunction is determined based on powers at which the at least one otherbase station is performing downlink transmissions in each of the one ormore sub-bands.
 51. The method of claim 48, wherein the information istransmitted by the first base station to the at least one other basestation over an X2 interface.
 52. The method of claim 48, wherein theinformation further comprises an indication for each of the one or moresub-bands indicating whether a transmit power of the first base stationfor at least one resource block for each of the one or more sub-bands isabove or below a particular RNTP threshold.
 53. The method of claim 48,further comprising: estimating a spectral efficiency for each of the oneor more sub-bands by the first base station.
 54. The method of claim 53,wherein estimating the spectral efficiency for a particular sub-bandfurther comprises: approximating the spectral efficiency by a powerfunction of a Channel Quality Indicator reported by a mobile deviceperforming measurements on the particular sub-band; and approximatingthe Channel Quality Indicator by a linear function of a Signal toInterference and Noise Ratio measured by the mobile device, wherein theSignal to Interference and Noise Ratio is measured in decibels.
 55. Themethod of claim 54, wherein the linear function includes a constantoffset term.
 56. A first base station comprising: a processor to executeinstructions, wherein executing the instructions causes the first basestation to perform operations comprising: determining, at the first basestation, sensitivity of a utility function of a cell served by the firstbase station to changes in transmission powers allocated to one or moresub-bands by at least one other base station that neighbors the firstbase station; and transmitting information from the first base stationto the at least one other base station, wherein the informationcomprises sensitivity information for the utility function for each ofthe one or more sub-bands and wherein the information is associated witha Relative Narrowband Transmit Power of the cell in each of one or moresub-bands.
 57. The first base station of claim 56, wherein thesensitivity of the utility function is determined based on path gainsbetween the first base station and transmitters of the at least oneother base station.
 58. The first base station of claim 56, wherein thesensitivity of the utility function is determined based on powers atwhich the at least one other base station is performing downlinktransmissions in each of the one or more sub-bands.
 59. The first basestation claim 56, wherein the transmitting by the first base station isperformed over an X2 interface.
 60. The first base station of claim 56,wherein the information further comprises an indication for each of theone or more sub-bands indicating whether a transmit power of the firstbase station for at least one resource block for each of the one or moresub-bands is above or below a particular RNTP threshold.
 61. The firstbase station of claim 56, wherein executing the instructions causes thefirst base station to perform further operations comprising: estimatinga spectral efficiency for each of the one or more sub-bands by the firstbase station.
 62. The first base station of claim 61, wherein estimatingthe spectral efficiency for a particular sub-band further comprises:approximating the spectral efficiency by a power function of a ChannelQuality Indicator reported by a mobile device performing measurements onthe particular sub-band; and approximating the Channel Quality Indicatorby a linear function of a Signal to Interference and Noise Ratiomeasured by the mobile device, wherein the Signal to Interference andNoise Ratio is measured in decibels.
 63. The first base station of claim62, wherein the linear function includes a constant offset term.